Tutor profile: Ankit B.
If 3Sin(x) + 4Cos(x) = 5 then find Cosec(x)? a. 2/3 b. 3/2 c. 3/5 d. 5/3
There are various ways you can attempt this question. The most basic technique to solve this and reach the answer is by converting the equation in terms of a single variable and solving it. Since we are aware of the basic identities relating Sin(x) and Cos(x), and also Sin(x) and Cosec(x), we can convert the equation in a single equation containing Sin(x) and solve the Quadratic equation. But here we can use our presence of mind to solve this quickly given we have the options. Now we all now that Cosec(x) cannot take values between -1 and 1 we can reject option a. and option c. directly. Assuming if Cosec(x) is 3/2, then Sin(x) is 2/3. Hence, by putting the value of Sin(x) in the equation, and also cos(x) in the same equation, we get that the Left Hand Side is not equal to the Right Hand Side. Therefore, the only option left is option d. which is the correct answer.
Subject: Basic Math
Basic Math becomes a part of a lot of Stress Interview situations especially for entry level analyst jobs. I have seen many of my friends and colleague complaining post interviews that they messed up with a simple 3-digit X 2-digit oral multiplication. Consider an example 367 X 63.
Now let us see how we can simplify this mentally and get the right answer quickly using simple expansion rules. First of all it is important to acknowledge that most of us won't be able to concentrate to visualise the entire conventional multiplication method in our heads. So there has to be a way around. My way of doing it is quickly breaking one of the numbers, so that we can transform the question into a summation exercise. Please note that I am not using any vedic mathematics techniques here. Take 63. We know that 63 can be written as 50 + 10 +3. This can be even simplified further to 100/2 + 10 + 3. So our problem now becomes 100/2 X 367 + 10 X 367 + 3 X 367. I have always liked multiplication and division with easy numbers like 2,3,5 and 10. So our problem becomes 36700/2 + 3670 + 367 X 3. But it might appear that even 367 X 3 is difficult. So we can simplify this further to 36700/2 + 3670 + 400 X 3 - 33 X 3 = 18350 + 3670 + 1200 - 99. When doing things mentally, it is always advisable that you ease your efforts and use your memory at the same time. Once you have all of it in addition or subtraction form, try not to use your conventional addition process in your mind, because its mistake prone. Instead, pick one number and with concentration solve it further. 21350 + 670 + 1200 - 99 = 22350 + 670 + 101 = 22451 + 670 = 23051 + 70 = 23121 While simplifying always follow your hunch on what appears simple. The interviewer knows that you obviously know the maths, but they are actually trying to check your composure in a pressure situation to deliver right result.
What is the most basic mistake a Startup enthusiast commits?
Most of the founders or Startup enthusiasts are good in building products, creating innovative solutions, using technology, etc. Since, they are so excited about heir field of expertise they end up deciding, sometimes even building a solution first and then start finding the problem for which the solution can be a fit. This is prevalent in most of the Mobile or Web based solutions since techies often start building an application or a software without identifying the problem, researching on it, figuring out the various possible solutions and customers, identifying the exact pain point and then jumping on the solution. The right way to do it is to go from a defined problem to a defined solution.
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